Over a round of golf this past weekend, Sen. Rand Paul asked President Donald Trump's blessing for a sensitive diplomatic mission.

Paul proposed sitting down with Iranian Foreign Minister Javad Zarif to extend a fresh olive branch on the president's behalf, according to four U.S. officials. The aim: to reduce tensions between the two countries. Trump signed off on the idea.

With Zarif in New York City this week for U.N. meetings and private sitdowns with journalists and think-tank experts, the prospect of the dovish Kentucky senator serving as the administration's chief diplomatic emissary has rankled many administration officials, who are expressing concern that Paul's intervention threatens to scuttle the president's "maximum pressure" campaign against Tehran.

It is unclear whether the senator will meet with Zarif. He and his office declined multiple requests for comment. But the president's willingness to tap Paul as the go-between with a top Iranian official is a demonstration both of his unorthodox approach to foreign affairs and his continuing desire, even as his aides threaten to squeeze Iran until it capitulates to U.S. demands, to entice the Islamic Republic's leaders to the negotiating table.